R. Basson, R. Lercier, C. Ritzenthaler, and
J Sijsling. An explicit expression of the Lüroth
invariant.
In Manuel Kauers, editor, Proceedings of the
38th International Symposium on Symbolic and Algebraic Computation, ISSAC
'13, pages 31-36, New York, NY, USA, 2013. Association for Computing
Machinery.
In this note, we give an algorithm to get an explicit
expression of the Lüroth invariant in terms of the
Dixmier-Ohno invariants. We also get the explicit factorized
expression on the locus of Ciani quartics in terms of the
coefficients. Finally, we answer two open questions on
sub-loci of singular Lüroth quartics.
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